Explanation

For a time series with quarterly seasonality (i.e., a seasonal pattern that repeats every 4 quarters), the appropriate method to remove the seasonal component is to use a 4-quarter moving average.

Why 4-quarter moving average?

• Quarterly seasonality means the pattern repeats every 4 periods (quarters)
• A moving average with the same length as the seasonal period (4 quarters) will smooth out the seasonal fluctuations
• The 4-quarter moving average effectively averages out the seasonal effects, leaving the trend and irregular components

Why other options are incorrect:

• Option B (2-quarter): Too short - would not capture the full seasonal cycle
• Option C (3-quarter): Wrong length - doesn't match the quarterly seasonal pattern
• Option D: Incorrect - moving averages are commonly used for deseasonalization

This is a fundamental concept in time series analysis where moving averages are used to remove seasonal patterns when the moving average length equals the seasonal period.